Correlation, entropy, and information transfer in black hole radiation

Abstract

Since the discovery of Hawking radiation, its consistency with quantum theory has been widely questioned. In the widely described picture, irrespective of what initial state a black hole starts with before collapsing, it eventually evolves into a thermal state of Hawking radiations after the black hole is exhausted. This scenario violates the principle of unitarity as required for quantum mechanics and leads to the acclaimed "information loss paradox". This paradox has become an obstacle or a reversed touchstone for any possible theory to unify the gravity and quantum mechanics. Based on the results from Hawking radiation as tunneling, we recently show that Hawking radiations can carry off all information about the collapsed matter in a black hole. After discovering the existence of information-carrying correlation, we show in great detail that entropy is conserved for Hawking radiation based on standard probability theory and statistics. We claim that information previously considered lost remains hidden inside Hawking radiation. More specifically, it is encoded into correlations between Hawking radiations. Our study thus establishes harmony between Harking radiation and the unitarity of quantum mechanics, which establishes the basis for a significant milestone towards resolving the long-standing information loss paradox. The paper provides a brief review of the exciting development on Hawking raidation. In addition to summarize our own work on this subject, we compare and address other related studies

Resolving the Information Paradox with Probabilistic Spacetime

“…A significant "correction" to Hawking's calculation demonstrated that the correlations between the subsystems of outside-the-BH radiation and of the radiation's inaccessible counterparts inside the BH offer a potential resolution to the D. M. Doren, J. Harasymiw information paradox [16] [17]. The researchers concluded these correlations account for additional encoded information and do so exactly to the degree that all information was previously thought lost.…”

“…No matter the size of the BH, its process of shrinking (which was seen as the cause of the information paradox) is exactly what ensures all internal probabilities eventually become external. (The two processes just described, being the encoded radiation and the more significant "relocating" of probabilities, are the PST's explanation of the mechanisms behind the previously reviewed finding that correlations between Hawking radiation and entangled BH entropy result in no loss of information [16] [17]. The main criticism found in that review was the lack of mechanism explaining how the correlation prevented information loss.)…”

Unruh effect and entropy of Schwarzschild black hole

“…Otherwise one is expected to take into account back-reaction as quantum gravity effects. From ( 5) we obtain (17) where in the 2nd line we used (13) and replaced summation with integral over the energies. Parameter N is omitted because it is completely defined by the spin s and by the observation time ∆ t , see (16) and the text below.…”

“…It leads to the possibility of information read-out from the region behind the event horizon due to the increasing contribution of quantum effects. Such a conclusion implies information preservation with BH, see [16,17], and might interfere with [18,19].…”

Tunneling across the quantum horizon does not resolve the information paradox

“…However, Parikh and Wilczek successfully incorporated the small back reaction effects during Hawking radiation to correctly estimate the radiation spectrum, proving it to be nonthermal [13]. Zhang et al claimed in a series of papers [14], [15], [16], [17], [18] that small corrections emerging from the nonthermality factors in the transmission amplitude of radiation quanta are sufficient to encode the black hole information as correlations among the radiated quanta. This intrigued a school of thought [19], [20], [21], [22] that promoted the results by Zhang et al as a possible resolution of the information loss paradox.…”